As shown in Fig. REF , we consider an integrated IRS-BS/AP architecture, where an antenna array and \(J=4\)  IRSs are deployed within a cuboid antenna radome, with \(\mathcal {J}\triangleq \lbrace 1,2,3,4\rbrace \)  denoting the set of all IRSs. Specifically, the BS's antenna array is deployed at the center of the back surface of the antenna radome, while IRSs 1–4 are respectively deployed at its left, right, top, and bottom surfaces perpendicular to the antenna array. We consider a three-dimensional (3D) local coordinate system (LCS) here, where the center of the antenna array is set as the origin \(O\) , and the antenna array is located on the \(x\) -\(O\) -\(z\)  plane. The antenna array is assumed to be a uniform planar array (UPA) with the size of \(M=M_{x} \times M_{z}\) , where \(M_{x}\)  and \(M_{z}\)  are the number of antennas along axes \(x\)  and \(z\) , respectively. The size of each IRS \(j\)  is denoted by \(N_{j}=N_{j,1} \times N_{j,2}\) , \(j\in \mathcal {J}\) , with \(N_{j,1}\)  and \(N_{j,2}\)  representing the number of reflecting elements along axes \(y\)  and \(z\)  (or \(x\) ), respectivelyIn practice, since the antenna radome of cellular BSs or WiFi APs has a limited size (e.g., in the order of several to tens of carrier wavelengths), the number of IRS reflecting elements that can be integrated into the antenna radome is limited. However, the distance between the IRSs and the antenna array of the BS is small, which can significantly reduce the path loss of the reflected signals by IRSs as compared to conventional IRSs deployed much farther away from the BS/AP [1]}, [2]}, [3]}.. The sets of elements for the BS UPA and IRS \(j\) , \(j \in \mathcal {J}\) , are denoted by \(\mathcal {M}\triangleq \lbrace 1,2,\cdots ,M\rbrace \)  and \(\mathcal {N}_{j}\triangleq \lbrace 1,2,\cdots ,N_{j}\rbrace \) , respectively. In the considered LCS, the location of the \(m\) -th antenna is denoted as \(\mbox{{$ s $}}_{m}=[s_{m,x},s_{m,y},s_{m,z}]^{T}\in \mathbb {R}^{3\times 1},~ m\in \mathcal {M}\) , and that of the \(n_{j}\) -th reflecting element of IRS \(j\)  is denoted as \(\mbox{{$ w $}}_{j,n_{j}}=[w_{j,n_{j},x},w_{j,n_{j},y},w_{j,n_{j},z}]^{T}\in \mathbb {R}^{3\times 1},~j\in \mathcal {J},~n_{j}\in \mathcal {N}_{j}\) . Since the IRS can only reflect signals to/from its front half-space, each IRS should be deployed to face the antenna array and all other IRSs so as to efficiently reflect signals to/from them. Denote \(\mbox{{$ \delta  $}}_{j}\)  as the normal vector of the plane which IRS \(j\)  is located in, with \(\Vert \mbox{{$ \delta  $}}_{j}\Vert =1,~j\in \mathcal {J}\) . According to the orientation of the IRSs, we have \(\mbox{{$ \delta  $}}_{1}=[-1,0,0]^{T}\) , \(\mbox{{$ \delta  $}}_{2}=[1,0,0]^{T}\) , \(\mbox{{$ \delta  $}}_{3}=[0,0,-1]^{T}\) , and \(\mbox{{$ \delta  $}}_{4}=[0,0,1]^{T}\) . Moreover, as shown in Fig. REF , the antenna radome is deployed at altitude \(H_{AR}\)  with a suspension angle of \(\theta _{tilt}\in [0,\pi /2]\)  with respect to (w.r.t.) the vertical direction (which is perpendicular to the ground). Note that the suspension angle \(\theta _{tilt}\)  can be adjusted according to the requirement of specific communication applications, such as \(\theta _{tilt}\in [0,\pi /12]\)  for cellular BSs [4]} (see Fig. REF (a)) and \(\theta _{tilt}=\pi /2\)  for WiFi APs mounted on the ceiling (see Fig. REF  (b)). In this paper, we focus on the uplink transmission from \(K\)  users to the BS, where the set of users is denoted by \(\mathcal {K}\triangleq \lbrace 1,2,\cdots ,K\rbrace \) .
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